Ratio and proportion word problems, step by step

A ratio is how a story compares two amounts, and a proportion is what lets you scale it.

The question

At that rate, how long will it take to stamp 300 tickets?

A press stamps 200 tickets every 4 minutes.
200 ÷ 4 = 50
200 ÷ 4 = 50
300 ÷ 50 = 6 minutes
asked:At that rate, how long will it take to stamp 300 tickets?
6 minutes
  1. Read it through once. Two things change TOGETHER at a fixed rate, so the trick is to find the rate for ONE unit first — everything the question asks scales from that.
  2. Find the rate for one: 200 ÷ 4 = 50. That is how much goes with a single unit.
  3. Now scale that rate of 50 to what the question asks: 300 ÷ 50 = 6 minutes.
  4. Answer the question that was asked — "At that rate, how long will it take to stamp 300 tickets?" — 6 minutes.

How it works.

  1. 01

    Read it through once. Two things change TOGETHER at a fixed rate, so the trick is to find the rate for ONE unit first — everything the question asks scales from that.

  2. 02

    Find the rate for one: 200 ÷ 4 = 50. That is how much goes with a single unit.

  3. 03

    Now scale that rate of 50 to what the question asks: 300 ÷ 50 = 6 minutes.

  4. 04

    Answer the question that was asked — "At that rate, how long will it take to stamp 300 tickets?" — 6 minutes.